Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000376
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000376: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
 => [[2,2],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,1,0,1,1,0,0,0]
 => [[3,3],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 2
[1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 2
[1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[1,1,0,1,1,0,0,1,0,0]
 => [[4,3],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [[4,4],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 2
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 2
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [[4,4,1],[3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 0
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => [1,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => [1]
 => [1,0,1,0]
 => 0
Description
The bounce deficit of a Dyck path. For a Dyck path $D$ of semilength $n$, this is defined as $$\binom{n}{2} - \operatorname{area}(D) - \operatorname{bounce}(D).$$ The zeta map [[Mp00032]] sends this statistic to the dinv deficit [[St000369]], both are thus equidistributed.
Matching statistic: St000741
Mapping
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 10%
Values
[1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1 = 0 + 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1 = 0 + 1
[1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1 + 1
[1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1 = 0 + 1
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1 = 0 + 1
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1 = 0 + 1
[1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(4,5)],6)
 => ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(3,6),(4,5)],7)
 => ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 2 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? = 1 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? = 1 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => ? = 2 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 1 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 1 = 0 + 1
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => ? = 0 + 1
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => ? = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(5,6)],7)
 => ? = 1 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(5,6)],7)
 => ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(5,6)],7)
 => ? = 2 + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(5,6)],7)
 => ? = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 1 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 1 + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => ? = 0 + 1
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => ([(2,9),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
 => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
 => ? = 3 + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => ? = 1 + 1
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => ? = 1 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(5,6)],7)
 => ? = 2 + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 + 1
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => ? = 1 + 1
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 2 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => ? = 1 + 1
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(5,6)],7)
 => ? = 2 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(5,6)],7)
 => ? = 2 + 1
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(5,6)],7)
 => ? = 3 + 1
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 1 = 0 + 1
Description
The Colin de Verdière graph invariant.
Matching statistic: St000982
Mapping
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00268: Binary words —zeros to flag zeros⟶ Binary words
St000982: Binary words ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 30%
Values
[1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 101100 => 010001 => 3 = 0 + 3
[1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 11001100 => 10111011 => 3 = 0 + 3
[1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => 10100001 => 4 = 1 + 3
[1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 10110010 => 10010001 => 3 = 0 + 3
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => 10111001 => 3 = 0 + 3
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => 10110001 => 3 = 0 + 3
[1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 11011000 => 10100011 => 3 = 0 + 3
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1110001100 => 0100010111 => 3 = 0 + 3
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1100111000 => 0101111011 => ? = 1 + 3
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 1100110010 => 0110111011 => ? = 0 + 3
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 1100101100 => 0100011011 => 3 = 0 + 3
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => 1100110100 => 0100111011 => ? = 0 + 3
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 1110011000 => 0101110111 => ? = 0 + 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1011110000 => 0101000001 => 5 = 2 + 3
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 1011100010 => 0110100001 => 4 = 1 + 3
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 1011001100 => 0100010001 => ? = 0 + 3
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 1011001010 => 0110010001 => ? = 0 + 3
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 1011100100 => 0100100001 => ? = 1 + 3
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 1010111000 => 0101111001 => ? = 2 + 3
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 1010110010 => 0110111001 => ? = 0 + 3
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => 0100011001 => ? = 0 + 3
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1010110100 => 0100111001 => ? = 0 + 3
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => 1011011000 => 0101110001 => 3 = 0 + 3
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => 1011010010 => 0110110001 => 3 = 0 + 3
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => 1011101000 => 0101100001 => ? = 1 + 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => 0100110001 => ? = 0 + 3
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 1101110000 => 0101000011 => ? = 1 + 3
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 1101100010 => 0110100011 => ? = 0 + 3
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 1101001100 => 0100010011 => ? = 0 + 3
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 1101100100 => 0100100011 => ? = 0 + 3
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 1110110000 => 0101000111 => 3 = 0 + 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1101011000 => 0101110011 => ? = 0 + 3
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => 1101101000 => 0101100011 => ? = 0 + 3
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 111100001100 => 101110101111 => ? = 0 + 3
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 111000111000 => 101000010111 => ? = 1 + 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 111000110010 => 100100010111 => ? = 0 + 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 111000101100 => 101110010111 => ? = 0 + 3
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => 111000110100 => 101100010111 => ? = 0 + 3
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 111100011000 => 101000101111 => ? = 0 + 3
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 110011110000 => 101011111011 => ? = 2 + 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 110011100010 => 100101111011 => ? = 1 + 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 110011001100 => 101110111011 => ? = 0 + 3
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 110011001010 => 100110111011 => ? = 0 + 3
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 110011100100 => 101101111011 => ? = 1 + 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 110010111000 => 101000011011 => ? = 2 + 3
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 110010110010 => 100100011011 => ? = 0 + 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => 110010101100 => 101110011011 => ? = 0 + 3
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => 110010110100 => 101100011011 => ? = 0 + 3
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => 110011011000 => 101000111011 => ? = 0 + 3
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => 110011010010 => 100100111011 => ? = 0 + 3
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => 110011101000 => 101001111011 => ? = 1 + 3
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => 110011010100 => 101100111011 => ? = 0 + 3
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 111001110000 => 101011110111 => ? = 1 + 3
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 111001100010 => 100101110111 => ? = 0 + 3
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => 111001001100 => 101110110111 => ? = 0 + 3
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => 111001100100 => 101101110111 => ? = 0 + 3
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 111100110000 => 101011101111 => ? = 0 + 3
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => 111001011000 => 101000110111 => ? = 0 + 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => 111001101000 => 101001110111 => ? = 0 + 3
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 101111100000 => 101010000001 => ? = 3 + 3
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 101111000010 => 100101000001 => ? = 2 + 3
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => 101110001100 => 101110100001 => 4 = 1 + 3
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 101110001010 => 100110100001 => ? = 1 + 3
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => 101111000100 => 101101000001 => ? = 2 + 3
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => 101100111000 => 101000010001 => ? = 2 + 3
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => 101100101100 => 101110010001 => 3 = 0 + 3
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 101010110100 => 101100011001 => 3 = 0 + 3
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => 101101100010 => 100101110001 => 3 = 0 + 3
[1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => 101101001010 => 100110110001 => 3 = 0 + 3
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => 101110110000 => 101011100001 => 4 = 1 + 3
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => 101110100100 => 101101100001 => 4 = 1 + 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => 101101101000 => 101001110001 => 3 = 0 + 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => 101101010100 => 101100110001 => 3 = 0 + 3
Description
The length of the longest constant subword.